Learning Math as an Experimental Science


What if math were learned as an experimental science where spreadsheets were our laboratories.

Keith Devlin wrote a fascinating biography called “The Man of Numbers” about Leonardo of Pisa. Leonardo is credited with bringing Arabic arithmetic and algebra to Europe. But his story is much more interesting and his lasting mark on not just mathematics but on education has long been overlooked. Leonardo was born in Pisa around 1170, when Pisa was the greatest trading city in Europe and had just begun building what we know of as the Leaning Tower. His father, a trader and diplomat for Pisa, brought Leonardo to Algeria when he was a boy and had him tutored in Arabic arithmetic and algebra. Leonardo became a merchant/trader traveling Africa and Eastern Asia. The mathematics of business in both Medieval Europe and the Muslim world was the Roman system using an abacus to perform calculations. But as Leonardo found, it was slow, cumbersome, and error prone. It worked for the Roman Empire which had a consistent monetary and weights and measures system. In Medieval Europe nearly every city-state had its own monetary and weights and measures system which meant that merchants had to constantly solve difficult ratio and proportion problems and equations.

So in 1200 Leonardo returned to Pisa and wrote Liber abacci The Book of Numbers, for merchants and traders to provide them with a revolutionary new arithmetic and algebra to solve their problems quickly and confidently. This book became the basis for the transformation of mathematics and business. Devlin included a picture of Leonardo’s “Table of Contents.” I was awestruck. The sequence of chapters in Liber abacci was a replica of the sequence we teach in K-12 math. The mathematics Leonardo developed for the needs of business in 1202 is the mathematics we now expect every child to master in K-12.

It is not the math business uses today!. For a business math revolution occurred in 1979 with the first personal computer spreadsheets. Spreadsheets are based on the mathematics of functions, first developed nearly 450 years after that enabled the scientific revolution and that has in the past 35 years transformed business. Leonardo’s rapid paper-based computation algorithms and equation solving is no longer necessary. Computers do that. Today business thinks in terms of input, outputs, and rules connecting them. Today business wants to ask of mathematics, What if…

Most of us have heard of Leonardo as Fibonacci, a nickname given him for unknown reasons eight centuries after he lived. His sequence was a minor diversion in his great work. Now his mathematics is obsolete, we no longer use most of it, and we no longer need our children to learn it.

I created this deck to help you envision math as an experimental science and spreadsheets as laboratories.

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To learn more go to What if Math.